“Everything and More” and related things
(Disclaimer: This turned into one of my . . . things where I rant on and on. Over 3000 words. Read at your own risk.)
I’ve been reading Everything and More, David Foster Wallace’s history of the concept of infinity. It received poor reviews from mathematically educated critics (including from some who liked Wallace’s fiction — see e.g. here), and I’m mainly reading it out of general interest in Wallace, rather than to learn about the material he presents.
So far it’s not much better than the reviews suggested. I admire Wallace’s attempts to present math in a fun and casual way (it reads very much like a transcript of a lecture from a wisecracking professor, as opposed to something composed for the page), but his famously digressive style is not well suited for math exposition. Worse, although a lot of the points he wants to make are basically valid, he presents them in an annoyingly arbitrary order, and muddles many of the key points by stating them in such a vague, terminologically inconsistent, and hand-wavey way that you basically have to be already familiar with the arguments in order to reconstruct them from Wallace’s versions of them. Wallace explicitly justifies his vagueness (repeatedly, to the point of being annoying) as a way of avoiding the technical thorniness that can make math unpleasant for general readers, but if this is really what he’s trying to do, it backfires horribly. I already know most of this stuff, and so I know how to translate Wallace’s sloppy verbal gestures into precise arguments (and when to ignore the occasional just-plain-wrong assertion or assumption), but I can’t imagine what a naive reader would think of all of this. It’s amazing how confusing Wallace manages to make some fairly simple ideas, all in the name of making them less confusing.
I don’t know much about the publication history surrounding this book, but (here I’m making a wild and kind of nasty conjecture) I feel like the very fact that it exists is a testament to a public misperception of Wallace, which ties into to common misperceptions of math itself. Let me be clear: I absolutely love Wallace as a writer. But I think a lot of the press he has received — especially the press he received during his lifetime — praised him for the wrong reasons. The standard line about Wallace before his death was that he was a “clever” writer, with a large vocabulary and a knack for mathematics, whose spiraling prose will seem either intoxicating or arrogant depending on one’s temperament. Only after his death did it become clear just how much Wallace’s depression had influenced his work throughout his life, and how much pain, insecurity and desperation had been woven into that famous “cleverness.”
This may be too biographical for some people’s tastes, but I personally think you can’t understand Wallace without knowing about his depression. I certainly didn’t; on my first encounter with Wallace’s essays I found them glib and pretentious, and I only became truly interested in him after reading D. T. Max’s New Yorker piece, which depicted an anxious, depressed, perpetually self-critical figure who was shockingly far from the smug, complacent Genius Grant recipient that the essays had caused me to imagine.
Which points to the basic tension in evaluation of Wallace’s work. On the one hand, he has a clear and acknowledged debt to a previous generation of reputedly clever and cold novelists — the postmodernists, black humorists, and metafictionists of midcentury. Again, there’s a typical line on this subject, which is that the difference between Wallace and these writers is that Wallace wanted to “move beyond” the dark comedy of their work to create a newer, more “sincere” sort of fiction. But it seems to me that, once you include the biographical in your purview, there’s a much more basic difference. The midcentury postmodernists, for all the darkness of their fiction, seem to have been placid, relatively happy people. Barth was famous for his so-called “sunny nihilism.” Nabokov was a cheerful pedant. We don’t know very much about Pynchon, but what we do know is pretty undramatic. Writers like these bring to mind the cliche that “life is a tragedy for those who feel, and a comedy for those who think.” Wallace, on the other hand, was pretty much the classic tortured artist.
Which should drastically affect our view of his use of “postmodernism” and “black comedy.” It seems to me that these concepts must have had more emotional valence for Wallace than they did for their originators. D. T. Max writes of Wallace:
When he returned to school, Wallace took his first creative-writing class, and began aggressively reading contemporary fiction. He was drawn to the postmodernists, whose affection for puzzles and mirrors-within-mirrors sensibility reflected his own enthusiasm for math and philosophy.
Wallace often spoke, rapturously, of the pleasure of doing math and analytic philosophy, where he relished the feeling of a solution “clicking” into place after many failed attempts. He must have experienced the same feeling while reading the complex creations of the postmodernists. And yet he was also a very depressed man who seemed to be desperately searching for some sort of palliative — a search that drove his interest in religion and his sentimental attachment to the concept of simple, humble work (the former addicts in Infinite Jest nobly living their sober lives “one day at a time”; the college slacker in The Pale King who has a life-changing experience when he stumbles into an accounting class by accident and hears a lecture on responsibility and the importance of “boring” work to society).
The mistake to avoid here is treating Wallace as though he is a postmodernist who just so happened to be depressed, rather than a depressed person who just so happened to like postmodernism. Infinite Jest isn’t supposed to be an encyclopedic (or “hysterical realist”) social novel or a survey of drug use (which makes criticisms of the book on that level ineffective). It’s a deeply personal, autobiographical book by a person in whose psychology concepts like “encyclopedicness” played an important role. The numerous references to math and philosophy in the book aren’t there out of a desire to be smart, or academic, or to write a novel that “treated” math as a subject. They’re there because the author liked math and philosophy and so of course a novel that consists of his tortured, quivering soul poured out on the page is going to involve a good deal of those subjects. Similarly, the dark comedy, the baroque and implausible plot, the Pynchonian names — these aren’t so much the attempts of a self-conscious craftsman to work in the tradition of postmodernism as they are the natural means of emotional expression for a person who really liked postmodern fiction. I don’t think I’m condescending to Wallace or diminishing his accomplishments by saying this, because I think it actually speaks to his success. Wallace is playing an entirely different game from much of his source material: rather than simply fiddling around with ideas, Wallace depicts psychological anguish, paralysis and ecstasy as experienced by someone who enjoys fiddling around with ideas.
His fiction isn’t concerned about math or metafiction in themselves — it’s concerned with what it’s like to be a depressed nerd. And he isn’t a slangier Pynchon — he’s a more analytically inclined Dostoyevsky.
Which brings us back to math. Because why has there been all this ink spilled about Wallace as a “clever,” “smart” novelist, anyway? Barth, Pynchon and Gaddis wrote tight, precise sentences that showed a dispassionate (hmm) mastery of English vocabulary. Wallace’s sentences are baggy, inefficient, full of strange usages that verge on being solecisms. His famous references to math and science lack the virtuosity of his peers’ delves into specialized language — if you know what he’s talking about, you’ll realize he’s making basic mistakes all over the place. (A reference to Cantor’s Diagonal Argument in Infinite Jest is hilarious but inaccurate; a famous conversation in the book about calculus includes several formulas and graphs, yet fails to make mathematical sense.) I’m not saying that Wallace’s writing is bad, but that focusing on its supposed academic merits ignores its real virtues, which lie in its depictions of psychological states, its eerie mimicry of the actual sound of moment-to-moment linguistic consciousness. (Which makes one hope for a moment that all those errors are really deliberate, intended to mimic the sloppiness of unedited thought — but then why do they persist in his sincere attempts at nonfictional exposition, like Everything and More?)
My guess is that Wallace got his reputation from one very simple fact: he was interested in math and the mathy side of philosophy. And our culture is just plain terrified of math. Artists who do ingenious things with language, or who display deep knowledge of history, are just doing what literary intellectuals expect each other to do. But give off the slightest indication that you know something about math or physics (or even chemistry) and the critics instantly regard you with a heady mix of fear, awe, insecurity, hyperbolic admiration, and condescension. My belief is that this is a historical accident, a result of the fact that we routinely subject our children to what amounts to state-funded, massive-scale aversion therapy for mathematics. From a very young age, we present to them a succession of boring, contextless, apparently meaningless puzzles and tell them that these puzzles are “math.” A few of them (the present writer included) will have the right sort of perverse, compulsive, quasi-masochistic personality to make this procedure seem like fun rather than torture; they become “good at math,” they lord it over everyone else, a hierarchy is established, and everyone else grows up hating “math” and the smirking, sweatpants-clad dweebs who actually take pleasure in it. Since elementary math is an extremely hierarchical subject — in order to learn any concept you have to have most of the concepts before it down cold — kids who have dropped off the ladder can’t get back on it again. Thinking you’re “bad at math” is a self-fulfilling prophecy: confusion over topic #n leads to despair which leads to not learning topic #n which makes you even more screwed when you get to topic #n+1, etc. It doesn’t get any better when you get old enough to be told that math is what makes our society go, and that if only you were interested in “hypotenuses” and “solving for x,” instead of actually interesting things like literature and history and music, you could grow up to be something useful like an engineer or a scientist.
It’s sad for two reasons. One of them is that math, and the science it enables, are jewels of modern civilization, astonishing creations that every educated person should know about. They are, among other things, how the modern world got to be so magical and intimidating, and it’s a shame that so many people spend their days staring at glowing boxes and zooming about in metal monstrosities without really understanding how these things work or the worldview that made them possible. It’s a shame that people are routinely taught that they live on a giant rock flying around a giant fireball, and that all of this is really a bunch of tiny superstrings or probability waves or something, without having any framework for interpreting and understanding these crazy tales. It’s a shame that our civilization is divided into a small group of self-important, blinkered technocrats who understand why the modern world is so weird and a vast, nebulously resentful mass of people who don’t. And plus, once you get beyond the really basic stuff, math is beautiful and fascinating and you learn why all the basic stuff mattered and how it all links up to the basic structure of the physical world and maybe to some deeper world beyond it. (But in the current setup, the only people who stick with math long enough to learn why it’s so great are the dorky faithful who need no convincing.) The second reason our mistreatment of math is sad is that basic math is really incredibly easy. I don’t know how to properly tell you this so you’ll believe it. I’m a math grad student, so of course it looks easy to me, right? Well, I’ve considered that, but I just don’t believe it. I really think that elementary math — by which I mean stuff up to and including what’s thought of as “college math” — is just an embarrassingly easy subject. You don’t have to consider the vast spiraling complexities of reality; you just have to learn a few simple rules, like learning a new board game. (In fact, it’s easier than board games; I’m terrible at board games; they’re so complicated and I’m very stupid; but math is nice and simple and easy, so even a dullard like me can understand it, even though anyone reading this can probably beat me in chess or scrabble.) The only reason we think this stuff is hard is that we teach it terribly, so terribly that it’s actually counterproductive. We end up convincing millions of people that they’re “bad at math” and giving them “math anxiety,” when really if they just looked at the rules of math with no preconceptions, as though they were the rules of a game, they would all be able to master it easily (seriously — once you get past the bullshit, it’s really that easy).
Just look, for instance, at what happens when we start teaching math in a way that isn’t unfathomably stupid. Look at those fucking graphs.
And so, to bring it back to Wallace, a society with all these unfortunate, unnecessarily complexes about math both praised Wallace too much and treated him as though he didn’t exist. They praised him too much because they acted as though the very fact he understood math (not at an especially high level, and not very well, from what I can tell) meant he was some sort of genius*. They treated him as though he didn’t exist insofar as they spoke as though Wallace’s references to math must be aspects of a “cold,” “clever,” “postmodern” “maximalism” rather than just references to stuff Wallace liked. No one would delve into math just for fun, right? And certainly math couldn’t have any emotional resonance for anyone . . . it couldn’t possible function as a pleasantly abstract escape from the horrors of clinical depression. No, you only go to math, as an author, if you want to be “clever.” Or “analytical.” Or some other cliche.
- DFW was a nerd with an amazing gift for depicting psychology in words and I love him.
- Everything and More kinda sucks.
- One day, our culture’s present attitude towards math will be looked back upon as pathological.
Oh, and one more thing I want to add. When I said that everyone can learn math, I don’t mean to entirely discount the idea of innate math ability. I just wanted to say that we’ve completely abused the notion in our ridiculous hand-wringing about how some kids have higher “aptitude” than others and this is somehow visible in fifth fucking grade when kids are being taught how to divide small integers or whatever. And in our ridiculous ideas about being good at math means “having a really high IQ” or “being able to rotate shapes incredibly fast in your head” or something, which are both kind of like saying being a good writer means being able to understand really long garden path sentences, or being really good at Scrabble, or something. There is such a thing as “innate math aptitude,” but it’s not some big bell curve — it’s a division between a few superheroes and the rest of us. I struggle, in my plodding dumb way, to learn and master college-type math, and so could most people if they’d had the right childhood experiences. But there are some people whose brains actually seem to come with specialized onboard processors that make all this stuff incredibly trivial, and let them absorb it all very quickly, and move on immediately to really hard math, the kind of stuff that my dismissals above did not include — the kind of stuff where I’ll be happy if one day I can understand the problems, to say nothing of helping mankind solve them.
There do tend, yes, to be a few people who contribute disproportionally to these cutting-edge efforts. It’s not too hard to tell when you’re dealing with one of them, because they tend, first of all, to be child prodigies. They absorb all the math that I personally know while still pubescent, and then they move on to the real stuff. I’m talking about people like Norbert Wiener (math B.A. at age 14, math/phil Ph.D. at age 17), or John von Neumann (who knew calculus — oh and Latin and Ancient Greek too — at age 8), or Richard Feynman (who, after learning calculus in his early teens, spent a lot of high school thinking about math and ended up reinventing some important modern math concepts). The list of concepts von Neumann is “known for” on his Wikipedia page is so long I’m not even going to try to count how many items are on it. Or how about Leonhard Euler, who influenced so many areas of math so deeply, back in the 18th century, that it’s impossible to imagine what modern math would have looked like without him? The messianic/extraterrestrial powers of these superhumans is so great that it makes the difference between people who are “good at math” and “not good at math,” in the merely pedestrian sense, look entirely meaningless. Every college math or physics major bows down before these guys. Very few academic researchers belong to this class — we just plod along, in our sorry little way, and leave the true revolutions to them. The point being that this vast gulf, almost as though between distinct species, makes any hand-wringing about differing levels of math aptitude and whether everyone is ready for the “rigors” of calculus look absolutely ridiculous.
*The same mechanism is what led critics to fawn over Tom Stoppard’s Arcadia, which presents a half-understood and over-simplified distillation of already distorted and simplified popular accounts of modern math like James Gleick’s Chaos. Errors like Stoppard’s and Wallace’s, in any other field, would be laughed down by intellectuals. But not in math.